Markov Chain Monte Carlo Estimation of Normal Ogive IRT Models in MATLAB

Abstract

Modeling the interaction between persons and items at the item level for binary response data, item response theory (IRT) models have been found useful in a wide variety of applications in various fields. This paper provides the requisite information and description of software that implements the Gibbs sampling procedures for the one-, two- and three-parameter normal ogive models. The software developed is written in the MATLAB package IRTuno. The package is flexible enough to allow a user the choice to simulate binary response data, set the number of total or burn-in iterations, specify starting values or prior distributions for model parameters, check convergence of the Markov chain, and obtain Bayesian fit statistics. Illustrative examples are provided to demonstrate and validate the use of the software package. The m-file v25i08.m is also provided as a guide for the user of the MCMC algorithms with the three dichotomous IRT models.

Keywords

• item response theory
• unidimensional normal orgive models
• MCMC
• Gibbs sampling
• Gelman-Rubin R
• Bayesian DIC
• MATLAB